High-dimensional counterdiabatic quantum computing

Abstract: The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we explore the extension of this paradigm to high-dimensional systems. Specifically, we consider qutrits in the context of quadratic problems, obtaining the qutrit Hamiltonian codifications and the counterdiabatic drivings. Our findings show that the use of qutrits can improve the quality of the solution up to 90 times compared to qubits counterpart. We test our proposal on 1000 random instances of the multi-way number partitioning, max 3-cut, and portfolio optimization problems, demonstrating that, in general, without prior knowledge, it is always better to use high-dimensional systems instead of qubits. Finally, considering the state-of-the-art in quantum platforms, we show the experimental feasibility of our high-dimensional counterdiabatic quantum algorithms at least in a full digital form. This work paves the way for the efficient codification of optimization problems in high-dimensional spaces and their efficient implementation using counterdiabatic quantum computing.